Question: Multiply the following complex numbers: $({3+5i}) \cdot ({-1+2i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({3+5i}) \cdot ({-1+2i}) = $ $ ({3} \cdot {-1}) + ({3} \cdot {2}i) + ({5}i \cdot {-1}) + ({5}i \cdot {2}i) $ Then simplify the terms: $ (-3) + (6i) + (-5i) + (10 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -3 + (6 - 5)i + 10i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -3 + (6 - 5)i - 10 $ The result is simplified: $ (-3 - 10) + (1i) = -13+i $